Goji Math-Thing-I-Need-a-Better-Title 1: 50 times this size...

g💚jira · November 14, 2014, 07:52:53 PM

Say we have two glasses. Let's call one of them A, and the other B. A has x mL of water [x∈R| x≥1]. B has x mL of soda. Got it? Now all that I'm going to do is take one mL of water from A and put it in B. Then I stir it until it mixes uniformly. I decide to backpedal a bit, and attempt to remove one mL of liquid from B and put it back in A. Of course, this is silly because the glasses' contents obviously aren't the same as before!

Question: What in particular can you notice in particular about the amount of contents of A and B at the end?

Dustin · November 14, 2014, 08:12:02 PM

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g💚jira · November 14, 2014, 08:12:53 PM

Quote from: Dustin on November 14, 2014, 08:12:02 PM

They're both mixes?

Dustin · November 14, 2014, 08:13:39 PM

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big sponge · November 14, 2014, 08:29:53 PM

No goji, you can not give me a quickie.

g💚jira · November 14, 2014, 08:36:04 PM

Quote from: Dustin on November 14, 2014, 08:13:39 PM

Quote from: GodspeedGojira! on November 14, 2014, 08:12:53 PM
Quote from: Dustin on November 14, 2014, 08:12:02 PM
They're both mixes?

Is the title supposed to hint at the answer?

Nah, it was me quoting Lord Hood from H2. 'cause glassing and Covenant and Reach and lasers

Quote

No goji, you can not give me a quickie.

lskjf

Dustin · November 14, 2014, 08:50:30 PM

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g💚jira · November 14, 2014, 08:58:45 PM

Quote from: Dustin on November 14, 2014, 08:50:30 PM

I feel like the answer you're looking for is a reference to some math theorem I wouldn't have any idea about.

Nah, it's solvable through simple math. Just gotta organize the solution/solution steps clearly. In the end one particular fact about the amount of liquids in each cup is made clear!

Dustin · November 14, 2014, 09:32:56 PM

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Dustin · November 14, 2014, 09:36:08 PM

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g💚jira · November 14, 2014, 09:36:18 PM

Quote

or someone intelligent replies.

Well you sort of posted that so

Spoiler

Quote from: Dustin on November 14, 2014, 09:32:56 PM

Quote from: GodspeedGojira! on November 14, 2014, 08:58:45 PM
Quote from: Dustin on November 14, 2014, 08:50:30 PM
I feel like the answer you're looking for is a reference to some math theorem I wouldn't have any idea about.

Nah, it's solvable through simple math. Just gotta organize the solution/solution steps clearly. In the end one particular fact about the amount of liquids in each cup is made clear!
Okay I have: Ax - A + 1 = Bx + A - 1; x = amount of liquid

I moved the equation around a bit but I'm not seeing anything significant.

How far off am I or should I just quit now?

Solution's a bit more complex than that XD [might wanna try arranging what happens at each step in a chart!]

Doctor Doom · November 14, 2014, 10:00:41 PM

They're wet.

rC · November 14, 2014, 10:17:52 PM

well soda is a bit more dense than water (right?), so glass b will weigh a little less than before you put the water in in the first place?

g💚jira · November 14, 2014, 10:20:10 PM

Quote from: RC5908 on November 14, 2014, 10:17:52 PM

well soda is a bit more dense than water (right?), so glass b will weigh a little less than before you put the water in in the first place?

It's got nothing to do with density/physics, it's just a very specific observation about the amount of liquid in each cup!

The Lord Slide Rule · November 14, 2014, 11:25:32 PM

So wait, did you mix the liquid from B back into A?

If so the ratio of soda to water in A should be approx. equal to the ratio of water to soda in B, no?

Dustin · November 14, 2014, 11:34:21 PM

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g💚jira · November 15, 2014, 02:46:35 AM

Quote from: SexyPiranha on November 14, 2014, 11:25:32 PM

So wait, did you mix the liquid from B back into A?

If so the ratio of soda to water in A should be approx. equal to the ratio of water to soda in B, no?

Well, it's exactly equal but close enough

Quote from: Dustin on November 14, 2014, 11:34:21 PM

Quote from: SexyPiranha on November 14, 2014, 11:25:32 PM
So wait, did you mix the liquid from B back into A?

If so the ratio of soda to water in A should be approx. equal to the ratio of water to soda in B, no?
If inversely equal... (but you already knew that I'm just trying to sound smart)

I was sort of thinking that too but Goji said it was complicated so I've been adding shit to this stupid equation that isn't fucking getting me anywhere.

Weeeelll by "complex" I meant you'd probably have to take a more elaborate approach to lay it out [more steps, not a bigger equation]. It waaaas still supposed to be a [relatively] basic problem! The actual problem is a formal proof but I decided against including that here... for now

—

Spoiler

Next: something to do with inequalities, maybe. Oh! I should totally do a breakdown of mathematical induction sometime too.

The Lord Slide Rule · November 15, 2014, 04:22:05 PM

Wait I got it?

g💚jira · November 15, 2014, 04:41:14 PM

Quote from: SexyPiranha on November 15, 2014, 04:22:05 PM

Wait I got it?

Mmhmm!

Actual question was to give a formal proof for it but that's another story for another time I guess XD

Spoiler

I might just do some small breakdowns of basic mathematical logic for people. Seems like people are interested in this stuff. And it's a way to keep me with math in Serious while still not breaching the Turkeyzone XD

The Lord Slide Rule · November 15, 2014, 04:43:14 PM

Quote from: GodspeedGojira! on November 15, 2014, 04:41:14 PM

Quote from: SexyPiranha on November 15, 2014, 04:22:05 PM
Wait I got it?

Mmhmm!

Actual question was to give a formal proof for it but that's another story for another time I guess XD

Spoiler
I might just do some small breakdowns of basic mathematical logic for people. Seems like people are interested in this stuff. And it's a way to keep me with math in Serious while still not breaching the Turkeyzone XD

I don't know a whole lot about formal proof. The one on mathematical inference could be fun.

Dustin · November 15, 2014, 04:43:14 PM

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Turkey · November 15, 2014, 05:09:25 PM

Quote from: GodspeedGojira!

I might just do some small breakdowns of basic mathematical logic for people. Seems like people are interested in this stuff. And it's a way to keep me with math in Serious while still not breaching the Turkeyzone XD

You can breach the Turkeyzone any time you want

Spoiler

I think you guys give me too much credit sometimes. I'm not a master of math, and I'm really weak on proofs.